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The algorithms that best demonstrate the potential of quantum computing are Shor's algorithm and Grover's algorithm. To this day, new evidence continues to emerge in the form of algorithms or ingenious applications that increase the field of application of this type of computing. However, given the limited number of qubits in current quantum computers, and also the noise problems they currently suffer from, implementing optimized circuits that allow us to take full advantage of the available resources, as well as detecting and correcting the errors caused by this noise, is a priority. In this work we present several leading zero detector circuits for quantum computers and simulators, optimized in terms of noise tolerance and number of qubits. These circuits are a fundamental part in major circuits that perform operations as important and basic in computation as addition and division. [ABSTRACT FROM AUTHOR]